Manager Steven Gerrard says beating Celtic was all about giving Rangers supporters Old Firm "bragging rights" for the first time in two years.
Ryan Jack's first-half goal took Rangers level on points with Celtic at the top of the Scottish Premiership.
They had not beaten Celtic in 12 games since winning the 2016 Scottish Cup semi-final on penalties and had not won a league derby since March 2012.
"This moment is about the fans. They've been through a lot," Gerrard said.
Rangers dominated the second meeting of the sides this season, having lost 1-0 at Celtic Park in September.
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Gerrard said the win over a side managed by his former Liverpool boss, Brendan Rodgers, would enable his team to "grow".
"The players were outstanding all over the pitch. I asked them to bring their A game and it was A-plus," he told Sky Sports.
"We'll get confidence and belief from it. We were outstanding all over the pitch, we were better to a man, and we could have won it more comfortably. We were superb.
"We played with courage, belief, we were brave and we competed all over the pitch."
Gerrard picked out midfielder Andy Halliday special praise, with the boyhood Rangers fan filling in at left-back.
"He epitomised the whole squad," the manager added. "He was outstanding against Hibs and earned the right to play.
"Andy Halliday is my unofficial captain, I think the world of him and he deserves his night."